Disordered Systems in Phase Space

TL;DR

This paper explores how phase space tools like Wehrl entropy reveal the transition from ballistic to localized regimes in disordered 1D and 2D systems modeled by Anderson localization, highlighting changes in wave function structure.

Contribution

It introduces phase space analysis, specifically Wehrl entropy, as a method to characterize the crossover regimes in disordered systems, providing new insights into wave function behavior.

Findings

Wehrl entropy detects the crossover from ballistic to localized regimes.

Phase space analysis distinguishes between chaotic and regular wave functions.

Results apply to 1D and 2D Anderson models.

Abstract

As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or regular behavior while diffusive conductors correspond to chaotic behavior. The chaotic or regular character of single wave functions can be inferred from phase space concepts like the Husimi distribution and the Wehrl entropy. These quantities provide useful information about the structure of states in disordered systems. We investigate the phase space structure of one dimensional (1d) and 2d disordered systems within the Anderson model. The Wehrl entropy of the eigenstates allows to detect the crossover between the ballistic, diffusive and localized regime.